Sparsity-Agnostic Lasso Bandit

TL;DR

This paper introduces a new sparse bandit algorithm that adapts to unknown sparsity levels, achieving tight regret bounds and outperforming existing methods in numerical evaluations.

Contribution

We propose a sparsity-agnostic algorithm for stochastic contextual bandits that does not require prior knowledge of the sparsity index and provides tight regret guarantees.

Findings

Our algorithm achieves tight regret bounds under mild conditions.

Numerical evaluations show it outperforms existing methods.

It remains effective even when the true sparsity is hidden from the algorithm.

Abstract

We consider a stochastic contextual bandit problem where the dimension $d$ of the feature vectors is potentially large, however, only a sparse subset of features of cardinality $s_0 \ll d$ affect the reward function. Essentially all existing algorithms for sparse bandits require a priori knowledge of the value of the sparsity index $s_0$. This knowledge is almost never available in practice, and misspecification of this parameter can lead to severe deterioration in the performance of existing methods. The main contribution of this paper is to propose an algorithm that does not require prior knowledge of the sparsity index $s_0$ and establish tight regret bounds on its performance under mild conditions. We also comprehensively evaluate our proposed algorithm numerically and show that it consistently outperforms existing methods, even when the correct sparsity index is revealed to them but is kept hidden from our algorithm.